An approximation theorem for continuous functions on Lp(1 ⩽ p < ∞) spaces including representation

The paper presents an approximation theorem, somewhat similar in content to Stone-Weierstrass theorem for continuous functions defined on Lp (1 ⩽ p < ∞) spaces. The result also includes an explicit representation of such functions. This result is useful for approximate representation of physical systems whose output depends continuously on its input data